Oh no. I haven't picked it up yet but I've paid for it. This was my concern. By fissures, do you mean cracks in a veneer?
Middle pic looks like scratches, bottom pic looks like fissure as Komo said. To hide scratches a wax crayon of corresponding colour can be rubbed over it. Also a wet used teabag works wonders as a temporary stain. Neither will harm the wood.
Hey Davey......that middle one looks like something came down on the drawer and cracked the lamination..
How long does the tea stain last? If that works for longer term then that's easier than trying to find the right colour crayon
Sounds better than splitting veneer. presumably can fill that with brown wax? I will take more photos when I have the piece.
That is what I usually do, I have a set of them in different wood colours. They also fill the area to some extent, which a teabag stain doesn't.